Answer
370
Work Step by Step
Using all seven letters = $\frac{7!}{3!.3!.1!}$ = 140
Using six letters we get a total of 20 + 60 + 60 = 140
3 O's and 3 S's = $\frac{6!}{3!.3!}$ = 20
3 O's , 2 S's and 1 R = $\frac{6!}{3!.2!.1!}$ = 60
2 O's , 3 S's and 1 R = $\frac{6!}{3!.2!.1!}$ = 60
Using five letters we get a total of 10 + 10 + 20 + 20 + 30 = 90
3 O's and 2 S's = $\frac{5!}{3!.2!}$ = 10
2 O's and 3 S's = $\frac{5!}{3!.2!}$ = 10
3 O's, 1 S and 1 R = $\frac{5!}{3!.1!.1!}$ = 20
3 S's, 1 O and 1 R = $\frac{5!}{3!.1!.1!}$ = 20
2'O , 2'S and 1 R = $\frac{5!}{2!.2!.1!}$ = 30
Total strings with five or more characters = 140 + 140 + 90 = 370
